Contents I. Introduction
Maxwell's equations, which represent a fundamental relationship between electric and magnetic fields, have been studied for decades. Although the analytical solutions have been given for many structures, it is not easy to obtain the analytical expressions for predicting the field behavior in the complex structures and composite materials. The alternative way is to use numerical techniques which have been under study and proven to be effective and efficient for solving Maxwell's equations in both time domain and frequency domain. With the particular desire of obtaining the full wave analysis, research has been driven into finding novel time domain techniques. The Finite-difference Time-domain (FDTD) method is one of the most popular time domain methods. It has been extensively studied and employed due to its simplicity, effectiveness and flexibility [1]. For the electrically large structures and highly conductive materials, however, the conventional FDTD algorithm requires large computation resources and prohibitively long simulation time owing to its two inherent limits: dispersion errors and the Courant-Friedrich-Levy (CFL) stability condition. Consequently, the recent FDTD-based algorithm developments have been aimed at removing or alleviating the two constraints. They include multiresolution time-domain (MRTD) method with low dispersion [2], pseudospectral time-domain (PSTD) method with great computation savings [3], and the recently developed unconditionally stable FDTD algorithms with the complete removal of CFL condition. In this paper, we will focus on the unconditionally stable algorithms.
